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Re: [Phys-l] Teaching Special Relativity

I don't have any trouble with introductions to special relativity based on time dilation, length contraction, and the relativity of simultaneity.* These are real kinematic effects that are all observable (with minor caveats) in principle and that can be shown to work together in truly delightful ways to produce a single reality that everyone agrees on.

The same cannot be said for "relativistic mass increase," which has no observational basis. What we observe is that objects moving at high speed have more momentum than that predicted by Newtonian mechanics. There are two possible responses to this fact: 1) let the mass of an object increase with velocity or 2) alter the dependence of momentum on mass and velocity.

In either case the correction is exceedingly simple and noticeable only at high velocities. The first response, however, leaves one with myriad difficult if not unresolvable questions: How does one actually measure the mass of a rapidly moving object? Where does the extra "stuff" come from? What about gravitational effects?

The second response sidesteps all of those problems. Why on Earth would anyone not choose it?

John Mallinckrodt
Cal Poly Pomona

*Nor do I, at least in principle, have any trouble with introductions based on the geometry of spacetime as John Denker compellingly advocates, although I haven't ever gone that route and probably won't.

Rick wrote:

I know I should just be quiet here and go ahead and do what I do (for a
couple more years), but here goes anyway.....

As usual, the Phys-L discussion, this time through on relativistic mass, has
two or more levels--the physics majors (maybe graduate level) and the intro
physics level. I won't address the former since I have never had to deal
with that (no physics majors, intro level courses only) in my 30 years of
teaching. What I will defend is the 'traditional' approach to special
relativity for intro courses, most especially those for non-science majors
(gen-ed).

At the outset we start with students (even science majors--chem & bio) who
are mostly Aristotilean thinkers. Giving the FCI to my chem/ engineering
students the first day of class shows this consistently. We work for the
most part of a semester to bring some fraction (reasonably large based on
the FCI retaken at the 1st semester exam) up to Newtonian thinking. That
is, we try to move the world view of students from a 300 BC up to the 18th
Century--in my case concentrating on MOTION as the focus. At this point I
(we) want to at least introduce the idea that Newtonian Physics, as useful
as it is even today, breaks down at high velocity or very small spatial
scales. The students are now thinking (hopefully) in Newtonian terms. So
how best to relay information about what relatitivity and quantum mechanics
change. We are not ready, willing, or able to consider making the students
fluent in 'modern physics' but don't want to close the book at Newtonian
Physics either.

In my mind (and obviously many others--including most authors) the way to do
this is to concentrate on the observational evidence and to do so from the
framework of a Newtonian world model. Here is where moving clocks run slow,
moving masses increase, and moving lengths contract come into play because
these 'apparent' effects are observable (at least two are.) The PSSC film
on muon lifetimes at Mt. Washington presents the time dilation evidence (and
deduces the length contraction evidence) quite nicely--I remember this film
from High School. There is annother PSSC film on bending electrons with
magnets and showing that the needed field that was seemingly linear in
momentum ceases to be so unless we look at the mass increasing with
velocity. [This may not be the 'correct' way to look at this according to
modern ideas, but it is an accessible way for our students.] Couple all
this with the non-simultaneity of events as viewed from different frames and
you have a fairly interesting, even exciting way to INTRODUCE special
relativity. One doesn't really have to speak of paradoxes--just
non-Newtonian effects. The travelling twin IS YOUNGER when he
returns---actually giving the 'possibility' of humans being able to travel
accross the galaxy--even between galaxies in a single 'lifetime'--- not much
of a possibility to be sure, but still a possibility. For Gen-Ed students
one doesn't even go into the math beyond showing things like the magnetic
field prediction from classical and relativistic calculations--not the full
calculations although that's OK for the science majors. The approach is
descriptive--here are the apparently 'strange' predictions of special
relativity when viewed from our Newtonian world and here are some
experimental results that display this behavior. I don't even touch on
General Relativity other than to relay the fact that GPS systems require its
use.

I have never been too concerned with advanced students having to 'unlearn'
someting--if really capable of advancing, they should be able to do this
handily. After all, we all learn and unlearn as we advance our levels of
understanding and models. I don't think anyone wants us to start out our
intro courses with 11-dimensional string theory, even if it is 'a model of
everything' including the origin of the Big Bang (as I just watched on the
Science Channel)! ;-)

Rick

***************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
******************************
Free Physics Software (including special relativity animations ;-)
PC & Mac
www.saintmarys.edu/~rtarara/software.html
*******************************


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